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A_i,j - A_j,i is a tensor

  1. Sep 24, 2006 #1
    prove that for any vector

    [tex]A_i[/tex]

    the expression

    [tex]A_{i.j}-A_{j.i}[/tex]

    is a tensor, even under non-linear transformations. Similarly prove that for any antisymmetric tensor

    [tex]E_{ij}[/tex]

    the expression

    [tex]E_{ij.k}+E_{jk.i}+E_{ki.j}[/tex]

    is a tensor.

    ____________________________

    What does the dots mean?
    For example between i and j in i.j ?
     
    Last edited: Sep 24, 2006
  2. jcsd
  3. Sep 25, 2006 #2

    dextercioby

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    Science Advisor
    Homework Helper

    Partial derivatives.

    Daniel.
     
  4. Sep 25, 2006 #3
    Thanks.
    I solved the problem except that about
    even under non-linear transformations.
    non-linear transformations from one set of coordinates to another?
    what changes if its non-linear transformations?
     
  5. Sep 25, 2006 #4
    Maybe non-linear means higher order terms in partials derivitives of the coordinates? They would cancel out in the examples given.
     
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